Rewrite as a simplified fraction. ${0.67\overline{3} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 673.3333...\\ 100x &= 67.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 606}$ ${x = \dfrac{606}{900}} $ ${x = \dfrac{101}{150}} $